Random Geometric Graphs as model of Wireless Sensor Networks

Wireless Sensor Networks (WSN) are likely to be widely deployed in the near future because they greatly extend our ability to monitor and control the physical environment. Finding a good network model for WSN is of great importance and has been the subject of several publications. Many models have their origin in classic areas of theoretical computer science and applied mathematics: regardless of the radio technology used, from the topology point of view, at any instant in time a WSN can be represented as a graph with a set of vertices consisting of the nodes of the network and a set of edges consisting of the links between the nodes. However, future applications will involve a large number of sensors to deploy on inaccessible areas, leading to a random deployment which makes the classical graph models obsolete. In this paper, we show that the random strategy is the only way to deploy future WSN and therefore the modeling with Random Geometric Graphs is the most appropriate.